Sets

[gmatmachoman]

Out of a total 85 children playing badminton or table tennis or both, total number or girls in the group is 70% of the total number of boys in the group. The number of boys playing only badminton is 50% of the number of boys and the total number of boys playing badminton is 60% of the total number of boys. The number of children playing only table tennis is 40% of the total number of children and a total of 12 children play badminton and table tennis both. What is the number of girls playing only badminton?

[harshavardhanc]

Out of a total 85 children playing badminton or table tennis or both, total number or girls in the group is 70% of the total number of boys in the group. The number of boys playing only badminton is 50% of the number of boys and the total number of boys playing badminton is 60% of the total number of boys. The number of children playing only table tennis is 40% of the total number of children and a total of 12 children play badminton and table tennis both. What is the number of girls playing only badminton?

girls/boys = 7/10

therefore, girls = (7/17) *85 = 35

and boys = 50

The number of boys playing only badminton is 50% of the number of boys = 25
the total number of boys playing badminton is 60% of the total number of boys = 30

so, 5 boys play both badminton and TT. ------- (1)

and boys who play only TT = 20.

The number of children playing only table tennis is 40% of the total number of children = 34
therefore, girls playing TT alone = 34-20 = 14.


a total of 12 children play badminton and table tennis both. -------(2)


from (1) and (2), girls who play both TT and badminton = 12-5 = 7.

therefore, girls who play just badminton [spoiler]= 35-7-14 = 14.[/spoiler]

what's the OA ?

[debmalya_dutta]

Total children = 85
total number or girls in the group is 70% of the total number of boys in the group
if x number of boys in group , then 0.7x number of girls => 0.7x+x =85
number of boys in group (x) = 50
number of girls in group (0.7x) = 35

The number of boys playing only badminton is 50% of the number of boys
=> number of boys playing only badminton = 0.5 * 50 = 25

The number of children playing only table tennis is 40% of the total number of children
=> number of boys + girls playing only TT = 0.4 * 85 = 34

total of 12 children play badminton and table tennis both

number of children who play only badminton = 85 - [ number of children who play only TT + number of children who play both]
number of children who play only badminton = 85- [ 43+12] =39

we already know that the number of boys who play only badminton = 25
=> the number of girls who play only badminton = 39-25=14
=> 85 = X + 34 -